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Mirrors > Home > ILE Home > Th. List > 2exsb | Unicode version |
Description: An equivalent expression for double existence. (Contributed by NM, 2-Feb-2005.) |
Ref | Expression |
---|---|
2exsb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exsb 1884 | . . . 4 | |
2 | 1 | exbii 1496 | . . 3 |
3 | excom 1554 | . . 3 | |
4 | 2, 3 | bitri 173 | . 2 |
5 | exsb 1884 | . . . 4 | |
6 | impexp 250 | . . . . . . . 8 | |
7 | 6 | albii 1359 | . . . . . . 7 |
8 | 19.21v 1753 | . . . . . . 7 | |
9 | 7, 8 | bitr2i 174 | . . . . . 6 |
10 | 9 | albii 1359 | . . . . 5 |
11 | 10 | exbii 1496 | . . . 4 |
12 | 5, 11 | bitri 173 | . . 3 |
13 | 12 | exbii 1496 | . 2 |
14 | excom 1554 | . 2 | |
15 | 4, 13, 14 | 3bitri 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wex 1381 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 |
This theorem depends on definitions: df-bi 110 df-sb 1646 |
This theorem is referenced by: (None) |
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